Four areas of theoretical population genetics will be studied. In the first, we will develop robust estimators for the time to the most recent common ancestor in a sample of DNA sequences. The objective is to find an estimator that works well when the sampled population has any demographic structure or history. After application to Y-chromosomal or mitochondrial DNA, modifications to allow for recombination will be introduced and the estimator tested on autosomal and X-linked sequences. The method is designed to apply to most of the commonly studied DNA variants. The second project studies the relationship between protein-protein interactions and the rate of evolution in yeast using published databases. We will investigate whether the interaction between proteins has a direct effect on evolutionary rate or if it is mediated by the relationship between fitness and evolutionary rate. In Project 3, we investigate two new models of genomic imprinting. The first is an X-Iinked version of our previous exact population genetic treatment. The second develops a three-variable quantitative inheritance structure with one variable as the level of activation of growth factor by a parent. The final project is devoted to three versions of the evolution of complexity. The first studies the fate of alleles at a gene that controls the level of epistatic interaction between other genes. The second extends our theoretical work on niche construction to models for the genetic effects on non-human species caused by human behaviors, such as use of antibiotics, that are culturally transmitted. The third aims to study the dynamics of linkage disequilibrium between genes that affect different culturally transmitted traits, with an application to sexual selection.